 | Euclides - 1848 - 52 pagine
...those angles equal which are opposite to the homologous sides. PROP. VII. THEOREM. If two triangles have one angle of the one equal to one angle of the other, and the sides about two other angles proportionals ; then, if each of the remaining angles be either... | |
 | 1851 - 268 pagine
...each side of it are similar to the whole triangle and to one another. PAPERS FOE THE SCHOOLHASTEB. 2. Equal triangles, which have one angle of the one equal to one angle of the other, have their sides about their equal angles reciprocally proportional. .3. Equiangular paralellograms have to one... | |
 | Harvey Goodwin - 1851 - 196 pagine
...to the sixth, the first shall have to the second a greater ratio than the fifth has to the sixth. 8. Equal triangles which have one angle of the one equal to one angle of the other have the sides about the equal angles reciprocally proportional ; and conversely. 9. If two planes which... | |
 | 1852 - 316 pagine
...2. About a given circle, to describe i triangle equiangular to a given triangle. 3. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals the triangles shall be equiangular, and shall have... | |
 | 1852 - 512 pagine
...the base, the triangles on each side of it are similar to the whole triangle and to one another. 2. Equal triangles which have one angle of the one equal to one angle of the other, have their sides about their equal angles reciprocally proportional. 3. Equiangular paralellograras have to one... | |
 | 1852 - 1080 pagine
...A c : A b : : A" E": A" F". Now it is demonstrated in treatises on geometry,* that if two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles are equiangular, and consequently... | |
 | Sir James Kay-Shuttleworth - 1853 - 554 pagine
...the base, the triangles on each side of it are similar to the whole triangle and to one another. 2. Equal triangles which have one angle of the one equal to one angle of the other, have their sides about their equal angles reciprocally proportional. 3. Equiangular parallelograms have to one... | |
 | Euclides - 1853 - 176 pagine
...other, have their sides about the equal angles reciprocally proportional ; and parallelograms that have one angle of the one equal to one angle of the other, and their sides about the equal angles reciprocally proportional, are equal to one another. LET ab,... | |
 | Royal Military Academy, Woolwich - 1853 - 400 pagine
...equiangular to the triangle DEF. Wherefore, if the sides, etc. QED PROPOSITION VI. THEOR. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have... | |
 | Euclides - 1853 - 334 pagine
...has been found a mean proportional HE. Which was to be done. PEOP. XIV. THEOE. If two parallelograms, which have one angle of the one equal to one angle of tie other, be equal : then they shall have their sides about this pair of equal angles reciprocally... | |
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If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar. 
